System and method for linearizing power amplifiers

ABSTRACT

A power encoder includes a pulse width modulator for modulating a signal according to a set of thresholds to produce a pulse width modulated (PWM) signal and a switch mode power amplifier for amplifying the PWM signal by switching states of switching devices according to amplitudes of the PWM signal. At least one or combination of a distribution of values of the voltage thresholds in the set and a distribution of values of a current generated by different switching devices are non-uniform. The set of voltage thresholds includes at least two positive voltage thresholds.

RELATED APPLICATION

This application is related to co-pending U.S. patent application Ser.No. 14/063,518 entitled “Digital power encoder for direct digital-RFtransmitter,” filed by Ma et al. on Oct. 25, 2013, and to U.S. patentapplication Ser. No. 14/063,543 entitled “System and Method forLinearizing Power Amplifiers,” filed by Ma et al. on Oct. 25, 2013 andincorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates generally to linearization of poweramplifiers, and more particularly to the linearization of a multi-leveldigital pulse-width-modulation encoder.

BACKGROUND OF THE INVENTION

A direct digital radio frequency (RF) transmitter (TX) has severaladvantages compared to the digital-analog-RF transmitters. The directdigital-RF transmitter arranges the digital-analog interface close tothe antenna, and thus fewer analog components are involved. Typicalanalog issues like In-phase (I) and Quadrature-phase (Q) signalsmismatch, local oscillator leakage, and image distortion can be largelyalleviated and even avoided. The direct digital-RF transmitter alsoenhances system flexibility through multi-mode and multi-band operationenabled by the agile digital signal processing. In addition, the directdigital-RF transmitter is digital friendly in nature, taking advantageof the increasing speed and density of digital processing as well ashigh-level integration. Thus, the direct digital-RF transmitters havebenefits for both wireless base-station and mobile applications.

The direct digital-RF transmitter includes a switching mode poweramplifier (SMPA), such as a class-D or class-S power amplifier,employing a particular power coding scheme, such as DSM (delta sigmamodulation), PWM (pulse width modulation) and PPM (pulse positionmodulation) in addition with a reconstruction band-pass filter (BPF).

In order to meet the stringent linearity requirement of modern wirelesscommunications system, most of the conventional SMPA-type transmittersuse DSM as the power encoder. Examples of such modulators includeband-pass delta-sigma modulation (BPDSM) based class-S power amplifiers.See, e.g., U.S. 2003/0210746, U.S. 2006/0188027, EP 2063536, and U.S.Pat. No. 7,825,724. The DSM is a noise shaping function with feedbackloops, which can increase the in-band noise to the out-of-band spectrum.The in-band signal-to-noise ratio (SNR) can be greater than 60 dB.

Although the high in-band SNR is desired, the near band quantizationnoise can increase abruptly. Therefore, an extremely high quality factor(Q) for BPF is required to let the filtered RF signal meet the spectrumemission mask. Furthermore, the DSM based direct digital-RF transmittercan cause the overall power inefficiency, due to the low power codingefficiency of the power encoder.

In terms of power, the RF power amplifier (PA) consumes the most energyin the transmitter. A main advantage of this transmitter is that theSMPA is always between ON (saturated) and OFF (cut-off) operatingregion, achieving high peak efficiency. However, if non-constantenvelope signals, which are common for 3^(rd) generation (3G) and 4^(th)generation (4G) cellular mobile communications systems, are encoded intothe single bit digitized signals, the in-band power over the entiredigitized signal power, defined as the power coding efficiency, is low,because the generation of quantization noise is inevitable and widelyspread throughout the frequency domain due to the noise shapingfunction, which is required from the system linearity specification.Because this noise signal is also amplified by the SMPA, the unwantednoise power becomes wasteful, which causes both excessive power loss andtotal TX efficiency degeneration.

The low power coding efficiency comes from the noise shaping in deltasigma power coding scheme. Alternatively, some conventional codingschemes use various PWM techniques to address the power codingefficiency. For example, some new high-efficiency power coding schemesbased on the PWM include RFPWM and 3-level polar PWM architecture.Because of the inherent nonlinearity of the PWM quantization, thelinearity performance degrades in the encoder. Both power coding schemesare built with analog high-speed comparators, which use the higherfrequency of triangular or saw-tooth waveform as the reference signal tobe compared.

EP2575309 discloses a pre-emphasis linearization block for a 3-level PWMpower coding scheme. The pre-emphasis block uses an inverse function ofthe transfer function of the RFPWM power coding. The output of thepre-emphasis block is submitted to the input of the RFPWM encoder.Ideally, the pre-emphasis can correct the nonlinearity by the RFPWMencoder. However, this is possible only when the inverse function existsand can be analytically derived.

For example, the system of EP2575309 uses relatively simple 3-level PWM,so the inverse function can be determined. However, for more than3-level, e.g., 5-level RFPWM encoding, the transfer function can becomeso complicated that no solution can be derived for its inverse function,which leads the difficulty to build the pre-emphasis block. Therefore,this method is not suitable for high frequency transmissions requiringcomplex encoding.

Hence, there is a demand for a new linearization method, particularlyfor the high power coding efficiency power encoder.

SUMMARY OF THE INVENTION

One objective of some embodiments of the invention is to compensate forthe non-linearity of the direct digital-RF transmitter, e.g., to meetthe specification for wide bandwidth high peak-to-average power ratio(PAPR) wireless communications signals.

Some embodiments of the invention are based on recognition that uniformdistribution of values of the voltage thresholds used by a pulse widthmodulator (PWM) for modulating a signal limits capability of modulatorto compensate for non-linearity of the signal and high-frequency noise.Some embodiments based on further realization and correspondingjustification that the power coding efficiency depends not only onstatistical property of the signal, but also on ratio of positive ornegative voltage thresholds. For example, in some embodiments, a ratioof two voltage thresholds is between 0.3 and 0.4. In one embodiment, theratio is 0.35.

Some embodiments of the invention are based on another recognition that,additionally or alternatively to the non-uniform distribution of voltagethresholds, a non-uniform distribution of values of a current generatedby different switching devices of a switch mode power amplifier (SWPA)for amplifying the modulated signal can also improve the efficiency ofthe power encoder. For example, in some embodiments, the modulatedsignal is a multi-level PWM signal and the ratio of the currentgenerated for one level of the modulated signal to the current generatedfor the next level of the modulated signal is between 0.2 and 0.4inclusively.

One embodiment uses both non-uniform distributions of the voltagethresholds and generated currents. The embodiment provides a way tooptimize the voltage and current distributions as well as pre-emphasislinearization, and improves the power coding efficiency by more than 5%.

Accordingly, one embodiment of the invention discloses a power encoderincluding a pulse width modulator for modulating a signal according to aset of thresholds including at least two positive voltage thresholds toproduce a pulse width modulated (PWM) signal; and a switch mode poweramplifier for amplifying the PWM signal by switching states of switchingdevices according to amplitudes of the PWM signal, wherein at least oneor combination of a distribution of values of the voltage thresholds inthe set and a distribution of values of a current generated by differentswitching devices are non-uniform.

Another embodiment discloses a method for power encoding includingmodulating a signal according to a set of thresholds including at leasttwo positive voltage thresholds to produce a pulse width modulated (PWM)signal; and amplifying the PWM signal by switching states of switchingdevices according to amplitudes of the PWM signal, wherein at least oneor combination of a distribution of values of the voltage thresholds inthe set and a distribution of values of a current generated by differentswitching devices are non-uniform.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1A is a block diagram of a power encoder employing linearizationaccording to some embodiments of the invention;

FIG. 1B is a block diagram of a pre-emphasis linearization methodaccording to some embodiments;

FIG. 1C is an example of a linearization mapping according to oneembodiment;

FIG. 2 is a block diagram of building and searching look-up table;

FIG. 3 is a circuit schematic of this direct digital-RF transmitterlinearization method based on look-up table as depicted in FIG. 2;

FIG. 4A is a schematic of determining the set of fixed thresholdsaccording to some embodiments of the invention;

FIG. 4B is a flow chart of this direct digital-RF transmitterlinearization method; and

FIG. 5 is a block diagram of the direct digital-RF transmitter accordingto some embodiments of the invention.

FIG. 6 is a block diagram of a power encoder according to someembodiments of the invention;

FIG. 7 is a schematic of a modulation of the signal with a set ofvoltage thresholds according to some embodiments of the invention;

FIG. 8 is a block diagram of a power encoder for producing the amplifiedoutput signal according to some embodiments of the invention;

FIG. 9 is a table showing different combination of ratios of voltagethresholds and generated currents for different levels of the PWM signalaccording to some embodiments of the invention; and

FIG. 10 is a flow chart of a method for dynamically selecting the set ofvoltage thresholds according to some embodiments of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Advanced switch-mode power amplifiers (SMPAs), e.g. class-S amplifiers,have become one of the key power amplifier architectures. The benefitsof high theoretical power efficiency and operational flexibility canenable next generation direct digital-radio frequency (RF) transmitter(TX) in mobile communications systems like software-defined radio (SDR).

The direct digital-RF transmitter utilizes class-S amplifiers to amplifya high-speed pulse-train generated via a power encoder, like delta sigmamodulator (DSM), pulse width modulator (PWM), or pulse positionmodulator (PPM). Usually a high-Q (>500) bandpass filter (BPF) is usedto reconstruct the signal back to analog RF. Notably, with the recentadvancement of Gallium nitride (GaN) RF transistor technology, thisarchitecture is gaining more attention, in particular forpico-/macro-base station cellular applications.

The pulse width modulators (PWM) are used for highly efficient switchingpower amplifiers, which are used for the amplification of radio signalsto be transmitted over an air interface in a wireless or wiredcommunications network. In principle, the PWM allows for an idealconversion of signals with continuous amplitude and limited bandwidth toa time continuous signal.

However, the PWM are inherently nonlinear, which results in thedistortion of the modulated signal. Thus, in order to maintain therequired integrity/linearity of the signals, especially for suppressingthe in-band noise floor and out-of-band image replicas, some embodimentsof the invention pre-distort the data signal before its quantization.

FIG. 1A shows a schematic 10 of power encoder with pre-emphasislinearization according to some embodiments of the invention. Anamplitude-phase splitter 11 splits an input signal 11 into an envelopesignal 111 and a phase modulated signal 109. The envelope signal 111represents amplitudes of the input signal, and the phase-modulatedsignal 109 represents phases of the input signal. A pre-distortion unit12 distorts the envelope signal 11 using a look-up table (LUT) toproduce a distorted envelope signal 121.

Some embodiments of the invention are based on recognition that atransformation function of PWM is nonlinear, but the input signal, e.g.,an envelope signal, has to be mapped linearly by the power encoder.Furthermore, the nonlinearity of the mapping depends on thetransformation function and cannot always be determined analytically.

Some embodiments are based on a realization that the nonlinearity of themapping can be determined experimentally by applying the transformationfunction to the input data and building a mapping, e.g., LUT, betweenthe data inputted to the power encoder and the data outputted by thepower encoding. It was further realized that it is possible topre-distort the input data based on the predetermined nonlinearitymapping, such that the transformation function of PWM transforms thepre-distort data to the value linear to the input data. To that end, theLUT stores a non-linear mapping of a transformation function used by PWM14 for the modulation, as described in more details below.

Because only amplitudes of the input signal have to be corrected, adigital converter 13 combines the distorted envelope signal 121 with thephase modulated signal 109 to produce a distorted input signal 131.Next, the PWM 14 modulates the distorted input signal according to thetransformation function to produce a modulated signal 141 and an SMPA 15amplifies the modulated signal 141 to produce a power encoded signal151. A relationship between the distorted input signal and the modulatedsignal is non-linear. However, because the distorted input signal wasdistorted based on the transformation function of the PWM, therelationship between the original input signal and the modulated signalbecomes substantially linear.

In one embodiment, the PWM is a radio frequency (RF) PWM (RFPWM), andthe digital converter up-converts the distorted envelope signal and thephase modulated signal with an RF carrier signal, such that themodulated signal is an RF pulse train. In alternative embodiment, thePWM is an intermediate frequency (IF) PWM (IFPWM), and the digitalconverter up-converts the distorted envelope signal and thephase-modulated signal with an IF carrier signal, such that themodulated signal is an IF pulse train. This embodiment can also includea second digital up-converter for converting the IF pulse train to an RFpulse train and for submitting the RF pulse train to the SMPA.

FIG. 1B shows a block diagram of a pre-emphasis linearization methodaccording to some embodiments. The method can be performed by aprocessor 100. The mapping, e.g., the LUT 135, is determined 130 using aforward mapping by applying the transformation function to a set ofinput data points. For example, the processor applies 120 thetransformation function 105 to the set of data points 115 of the inputto produce output data 125. The transfer function can be theamplitude-to-amplitude (AM-AM) transfer function. The LUT 135 isdetermined 130 as a mapping between the input 110 and the output 125 ofthe transformation.

In contrast, the distorted data is determined by a backward mapping ofthe data point of the envelope signal by selecting 140 using the LUT 135an input to the transformation function corresponding to an output ofthe transformation function that is equal to the data point of theenvelope signal.

For example, the input data received for processing by the power encoderare distorted 140 using the LUT 135 to produce the distorted data. Thedistorted data 145 is subsequently encoded by the power encoder toproduce encoded data, that are linear with the input data. The backwardmapping is performed for a set of data points of the input signal, suchthat each data point of the distorted input signal 145 equals to aninput to the transformation function corresponding to an output of thetransformation function that is equal to the data point of the inputsignal.

FIG. 1C shows an example of the backward mapping using the LUT 135according to one embodiment. The LUT 135 maps the input X with theoutput Y of the transformation. Various embodiments of the invention usethe LUT 135 to pre-distort the input signal before the power encoding.For example, the data point y′ 136 of the envelope signal is mapped 137to the value x′ 138. The value 138 is the pre-distorted value of thecorresponding data point of the distorted envelope signal and ismodulated with an aim to produce the linear mapping between the datapoint 136 of the envelope signal and the corresponding point of themodulated signal.

FIG. 2 illustrates a diagram of a method for determining the LUT 24according to some embodiments of the invention. In some embodiments theLUT 24 is determined adaptively for each portion of the input signal,e.g., a frame. In order to build the LUT 24, the AM-AM transfer function23 of the multi-level quantizer needs to be derived first. For a general(2N+1)-level quantizer, the amplitude-to-amplitude (AM-AM) transferfunction can be

$\begin{matrix}{{{f( {a(t)} )} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{\cos\lbrack {\sin^{- 1}( \frac{V_{thi}}{a(t)} )} \rbrack}}}},{{a(t)} \geq V_{thN}}} & (1)\end{matrix}$where a(t) is the envelope of the input data, and V_(thi) is the i^(th)threshold value, V_(thi)<V_(thj) when 1≦i<j≦N.

Next, the embodiments index the discrete LUT. The output vector Y is theresult calculated from the AM-AM function with the defined input vectorX, e.g., from V_(th1) to 1 with the fixed step, e.g. 0.001. Thisprocedure is accomplished by building the index 22 after thenormalization 21 of the envelope. Now, the LUT 24 is reversely searchedwith the envelope input Y′ to select the closest pre-distorted outputX′. Another gain block 25 can re-normalize the pre-distorted output tobe the input of the following power encoder.

The LUT 24 can be composed to describe the inverse behavior of thenonlinearity of the encoder, which is described in Equation (1).Pre-distortion procedure can be imposed according to the searched LUTvalue. This LUT searching algorithm has in theory no limitation on thenumber of quantization level, which is an advantage over the analyticalinverse function based pre-distortion scheme.

FIG. 3 shows a block diagram of a method for considering SMPAnonlinearity according to an embodiment of this invention. A directdigital-RF transmitter linearization method 30 includes thelinearization of both multi-level power encoder 35 and SMPA 37. Aprimary portion of this transmitter distortion correction is realized bythe high speed digital logic integrated circuit (preferablyapplication-specific integrated circuit: ASIC), which includes twoadders 39, amplitude-phase splitter 31, LUT 32, digital encoder 34, anddigital down converter (DDC) 38. Within the digital encoder 34, thereare two frequency up-converters 33 and 36, and a multi-level IFPWM(ML-IFPWM) 35.

Some embodiments of the invention are based on a realization that bydecreasing the PWM input carrier to an IF, and then encoding the IFsignals by a PWM, the time-domain quantization is extended and amagnitude of the quantization increased. Thus, the accessible clock rateof current digital processors can implement this power coding algorithmand the direct digital output to SMPA becomes realizable.

The first up-converter 33 converts the pre-distorted envelope to an IF,and then feeds the ML-IFPWM 35. The encoded result is furtherup-converted to RF by the second up-converter 36. In the preferredembodiment transmitter 30, the power amplifier 37 is a switching poweramplifier (preferably class-S PA module) that accepts a multi-levelpulse train as an input, and amplifies the high-speed pulse train signalincluding the necessary in-band information.

Part of the SMPA 37 output is coupled and digitized back to the digitaldown converter (DDC) 38, which down-converts the RF signal back to thebaseband as the feedback data. The input data can be aligned with thefeedback through a delay block 310. The lower combiner 391 determinesthe error data 392 that are subtracted from the input data in advance bythe upper combiner 393 to produce the corrected data 394. This feedbackloop corrects the distortion of the SMPA 37. The envelope of thecorrected data is calculated by the amplitude-phase splitter 31(preferably a coordinate rotation digital computer: CORDIC). The blockLUT 32 pre-distorts the envelope to correct the distortion of theML-IFPWM 35.

FIG. 4A shows a schematic of a method for determining the set of fixedthresholds, which is adaptive to each transmitted frame or subframeaccording to some embodiments of the invention. The method can beimplemented by a processor 40 connected to a memory 42. The basebandinput data 41 of a frame are stored in a memory 42 as vectors or arrays.Then, the processor 40 determines 43 the probability density function(PDF) 44 from data in the frame. The PDF is integrated 45 to generate acurve 46 of the cumulative distribution function (CDF). From the CDFcurve 46, a set of threshold values 48 are selected, e.g., the CDF curveis equally spaced. This process is adaptively repeated 49 frame by frameto ensure the set of thresholds 48 remains optimal.

FIG. 4B shows a flow chart 400 of the linearization method according toanother embodiment of the invention. The embodiment determines 401 thecorrected data by subtracting the input data and the error 409determined using a feedback 410 and extracts 402 the envelope of thecorrected data. The PDF 403 and the CDF 404 of the envelope aredetermined. Given the CDF, a set of threshold values for eachquantization levels is selected 405 from the CDF curve. The AM-AMtransfer function 406 and the LUT 407 are determined as described above,and used to pre-distort 408 the envelope of the input data throughsearching the LUT 407. The steps are adaptively repeated frame-by-frameto ensure that the power coding efficiency is always optimized. Thepower encoder 412 encodes the pre-distorted data and output to the poweramplifier 411 for transmitting. A small portion of power can also be fedback 410 to calculate the distortion error due to the power amplifier411.

FIG. 5 shows a block diagram of the direct digital-RF transmitter 50according to some embodiments. In these embodiments, a pre-distortionblock based on a LUT is arranged before the encoder to furthercompensate for the non-linearity. After the encoder, a 4-phase LO isemployed to up-convert the IF IQ signal into RF band. Hence, thisembodiment is a two-stage digital up-conversion at a reduced samplingrate. Because this is a pipeline architecture, the embodiments can use aparallel implementation to increase the sampling rate for higher timedomain quantization to achieve the desired linearity.

The input data are complex and includes both In-phase (I) andQuadrature-phase (Q) paths. The complex input is processed by acoordinate rotation digital computer (CORDIC) block 51 to convert theCartesian data to polar data (i.e., envelope (ENV) and phase θ). A LUTpre-distortion unit 52 is enabled to pre-distort the ENV for linearitycorrection of the nonlinear ML-IFPWM 54 power encoder. The output isnoted as PRE. The phase modulator 56 generates the phase modulation (PM)IQ signal (LO_(IFI) and LO_(IFQ)) at the IF carrier frequency (e.g.,100-MHz for LTE application). Two IF digital up-converters (DUCs) 53 mixthe PRE with LO_(IFI) and LO_(IFQ), respectively.

The output of the IF DUCs 53 IF, and IFQ are encoded by two ML-IFPWMpower encoders 54, e.g., shown in FIG. 3. The generated pulse trains arePWM_(I) and PWM_(Q). Another set of digital up-converters mix PWM_(I)and PWM_(Q) with LO_(RFI) {(1,0,−0,0, . . . } and LO_(RFQ) {0,1,0,−1, .. . }, respectively. The products are added by the combiner 55 to outputRF_(in). (i.e., RF_(in)=PWM_(I)·LO_(RFI)+PWM_(Q)·LO_(RFQ)) and then amapper 57 converts the multi-level RF_(in) into the control bits signal.

Usually, a (2M−1)-level pulse train needs M control bits, for instance,2 bits for 3-level and 3 bits for 5-level IFPWM signal. The M controlbits are binary switching signal SW(0:M−1) to control the switches(e.g., using GaN transistors) of the power amplifier (e.g., class-S PA)in 59. To fit the multi-bits input, the power amplifier can beconfigured in H-bridge for 3-level signal, or the paralleled H-bridgefor 5 or more-level signal.

There can be also a feedback from the output of the power amplifier. Thefeedback couples a small amount of power back to the input forcharacterizing the nonlinearity introduced by the power amplifier.Before the power amplifier, a buffer driver 58 is required tosynchronize the multi-bits input and also provide some amplification toreach the power amplifier's input power requirement. Within 59, abandpass reconstruction filter (BPF) can also be included in the SMPAmodule for filtering the out-of-band quantization noise in order totransmit the clean analog RF_(out), and, e.g., the BPF or anotheradditional designed energy recycling block (e.g. broadband RF-DCrectifier) can recycle RF power associated with those undesired spectralcomponents back to the SMPA DC supply. The RF_(out) is suitable fortransmission by an antenna. Other conventional transmitter and receivercomponents can also be used, e.g., an isolator to eliminate the effectof power reflections.

Non-Uniform Distribution Values for Power Coding Efficiency

FIG. 6 shows a block diagram of a power encoder 600 according to someembodiments of the invention. The power encoder 600 includes a pulsewidth modulator 610 for modulating a signal 630 according to a set ofvoltage thresholds 620 having including at least two positive voltagethresholds to produce a pulse width modulated (PWM) signal 615. In oneembodiment, the modulator is a radio frequency (RF) modulator, and thePWM signal is an RF pulse train. In alternative embodiment, themodulator is an intermediate frequency (IF) modulator, and the PWMsignal is an IF pulse train.

The power encoder 600 also includes a switch mode power amplifier (SMPA)640 for amplifying the PWM signal 615 to produce an output signal 645.The output signal 645 is produced by switching states of switchingdevices 650 of the SMPA according to amplitudes of the PWM signal. Invarious embodiments of the invention, at least one or combination of adistribution of values of the voltage thresholds 620 and a distributionof values of a current generated by different switching devices 650 arenon-uniform.

Some embodiments of the invention are based on recognition that uniformdistribution of values of the voltage thresholds used by a pulse widthmodulator for modulating a signal limits capability of modulator tocompensate for non-linearity of the signal and high-frequency noise.Some embodiments based on further realization and correspondingjustification that the power coding efficiency depends not only onstatistical property of the signal, but also on ratio of positive ornegative voltage thresholds. For example, in some embodiments, a ratioof two voltage thresholds is between 0.3 and 0.4. In one embodiment, theratio is 0.35.

FIG. 7 shows a schematic illustrating a modulation of the signal 710with a set of voltage thresholds 715 including five values −V₂, −V₁, V₀,V₁ and V₂ to produce a five-level PWM signal 720 according to someembodiments of the invention. As can be seen from FIG. 7, the selectionof the values of the voltage thresholds governs the presence and thelength, e.g., W₁ and W₂, of the constant amplitude values of the PWMsignal 720.

In some embodiments of the invention, the distribution of the values ofthe voltage thresholds 715 is non-uniform. Specifically, the distancebetween neighboring voltage threshold varies. For example, for twopositive thresholds, i.e., the first voltage threshold V₁ and the secondvoltage threshold V₂, the distance 740 between the values of theneighboring voltage thresholds V₀ and V₁ does not equal the distance 730between values of the neighboring voltage thresholds V₂ and V₁. Forexample, a ratio a_(v)=V₁/V₂ can be between 0.3 and 0.4 inclusively,e.g., a_(v)=0.35.

Some embodiments of the invention are based on another recognition that,additionally or alternatively to the non-uniform distribution of voltagethresholds, a non-uniform distribution of values of a current generatedby different switching devices of the SWPA for amplifying the modulatedsignal can also improve the efficiency of the power encoder. Forexample, in some embodiments, the modulated signal is a multi-level PWMsignal and the ratio of the current generated for one level of themodulated signal to the current generated for the next level of themodulated signal is between 0.2 and 0.4 inclusively.

FIG. 8 shows a block diagram of the SMPA 810 for producing the amplifiedoutput signal 815 by switching states of switching devices, e.g., theswitching devices 820, according to amplitudes of the PWM signal. Insome embodiments, a number of switching devices in the SMPA 810 dependson a number of voltage thresholds in the set 715. For example, in oneembodiment the PWM signal has (2n+1) levels, n is a positive naturalnumber, wherein the set of thresholds includes n non-zero values ofvoltage thresholds, and the SMPA includes 2n switching devices withnon-uniform total current capability for the n non-zero levels of thePWM signal.

The amplitudes of PWM signal 720 are converted by the mapper 830 intothe control signal. For example, for the five-level PWM signal, themapper 830 can include eight ON/OFF switches to map or transform the PWMsignal into a control bits signal. To fit the multi-bits input, thepower amplifier 810 can be configured in H-bridge for 3-level signal, orthe paralleled H-bridge for 5 or more-level signal.

In some embodiments, a distribution of values of a current generated bydifferent switching devices is non-uniform. For example, in someembodiments, the switching devices 820 are transistors having differentdimensions to produce different currents. For example, the transistorscan be GaN transistors with different width of the gates.

In one embodiment, the power amplifier includes 2n switching devices forthe n non-zero levels of the PWM signal to produce I_(n) current foreach level, wherein a ratio a_(v)=V_(n-1)/V_(n) and a ratioa_(i)=I_(n-1)/(I_(n-1)+I_(n)) are between 0.2 and 0.4 inclusively. Forexample, the power amplifier includes a first switching device forgenerating a current with a first value I₁, such that the poweramplifier produces I₁ current for the first level of the PWM signal andincludes a second switching device for generating a current with asecond value I₂, such that the power amplifier produces I₁+I₂ currentfor the second level of the PWM signal, wherein a ratio a_(i)=I₁/(I₁+I₂)is between 0.2 and 0.4 inclusively.

FIG. 9 shows a table with different combination of ratios 910 of voltagethresholds and generated currents for different levels of the PWMsignal. According to this table, one embodiment improves the powercoding efficiency with a combination 920 of non-uniform distributions ofthe values of the voltage thresholds and generated currents. Theembodiment improves the power coding efficiency by more than 5%.

For example, in one embodiment, the set of threshold includes the firstvoltage threshold V₁ for the first level of the PWM signal and thesecond voltage threshold V₂ for the second level of the PWM signal,wherein a ratio a_(v)=V₁/V₂ is between 0.3 and 0.4 inclusively. Also,the power amplifier includes the first switching device for generating acurrent with the first value I₁, such that the power amplifier producesI₁ current for the first level of the PWM signal, wherein the poweramplifier includes the second switching device for generating a currentwith the second value I₂, such that the power amplifier produces I₁+I₂current for the second level of the PWM signal, wherein a ratioa_(i)=I₁/(I₁+I₂) is between 0.2 and 0.4 inclusively.

Dynamic Updates for Power Codding Efficiency

For 3-level fixed threshold PWM, the theoretical power coding efficiencyis:

$\begin{matrix}{{\eta_{CODE} = \frac{\frac{1}{2}{\int_{0}^{1}{x^{2}{f_{x}(x)}\ {\mathbb{d}x}}}}{\int_{0}^{1}{\lbrack {1 - {\frac{2}{\pi}{\cos^{- 1}( \frac{x}{4/\pi} )}}} \rbrack{f_{x}(x)}\ {\mathbb{d}x}}}},} & (1)\end{matrix}$where x is the original baseband signal amplitude,

${f_{x}(x)} = {\frac{x}{\sigma^{2}}{\mathbb{e}}^{- \frac{x^{2}}{2\sigma^{2}}}}$is the PDF of x fitted by Rayleigh distribution.

For 5-level fixed threshold PWM, the theoretical power coding efficiencyis:

$\begin{matrix}{{\eta_{CODE} = \frac{\frac{1}{2}{\int_{0}^{1}{x^{2}{f_{x}(x)}\ {\mathbb{d}x}}}}{{\frac{1}{4}{E\lbrack {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{1}}{a} )}}} \rbrack}} + {\frac{3}{4}{\underset{a > V_{2}}{E}\lbrack {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{2}}{a} )}}} \rbrack}}}},} & ( {2a} ) \\{a = \{ {\begin{matrix}{{V_{1}\frac{1}{\sqrt{1 - ( {\frac{\pi}{2}x} )^{2}}}},} & {0 \leq x \leq x_{0}} \\{{V_{1}\frac{\sqrt{1 + \alpha^{2} + {\frac{4}{\pi\; x}\sqrt{( {1 - \alpha^{2}} )^{2} + ( {\frac{\pi}{2}x\;\alpha} )^{2}}}}}{\alpha\sqrt{2^{2} - ( {\frac{\pi}{2}x} )^{2}}}},} & {x_{0} < x \leq \frac{4}{\pi}}\end{matrix},} } & ( {2b} )\end{matrix}$where x is the original baseband signal amplitude,

${f_{x}(x)} = {\frac{x}{\sigma^{2}}{\mathbb{e}}^{- \frac{x^{2}}{2\sigma^{2}}}}$is the PDF of x fitted by Rayleigh distribution, a is the pre-distortedamplitude, V₁ and V₂ are two thresholds (V₁<V₂), their ratio

${\alpha = \frac{V_{1}}{V_{2}}},$and

$x_{0} = {\frac{2}{\pi}{\sqrt{1 - \alpha^{2}}.}}$

In the Equation (1), n_(CODE) is only associated with input signal'sf_(x)(x), therefore, any threshold value leads to the same power codingefficiency, which is around 46% for this LTE baseband signal. In theEquations (2a) and (2b), η_(CODE) is not only related to the inputsignal's f_(x)(x), but also the thresholds value ratio α. And thereexists an optimum solution: when α=0.3˜0.4, the power coding efficiencyis maximized to around 77%. Furthermore, more analysis shows that,α=0.35 can apply to almost all Rayleigh distributed signal patterns forfive-level PWM as long as the fitted scale parameter of the distributionσ=0.1, 0.2, . . . , 0.9, and that maximize power coding efficiency.

In some digital implementation of embodiments of the invention, theabsolute values of two thresholds are selected not too large or toosmall in order to make the best of the sampling resolution and notdegrade the linearity performance.

The modulated pulse width W of a 3-level PWM signal can be representedas,

$\begin{matrix}{{W(a)} = \{ {\begin{matrix}{{\frac{1}{2\; f_{c}}\lbrack {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V}{a} )}}} \rbrack},} & {a \geq V} \\{0,} & {a < V}\end{matrix},} } & (3)\end{matrix}$where f_(c) is signal's carrier frequency, a is the instantaneousenvelope in each period, and v is the threshold value in the set 715.For any PWM signal with steady state width W, whose fundamentalharmonic's amplitude is

$\begin{matrix}{{x(a)} = {\frac{4}{\pi} \cdot {{\sin( {\pi \cdot f_{c} \cdot {W(a)}} )}.}}} & (4)\end{matrix}$

Plugging Equation (3) into Equation (4) results in AM-AM function

$\begin{matrix}{{x(a)} = \{ {\begin{matrix}{0,} & {0 \leq a < V} \\{{\frac{4}{\pi} \cdot {\cos\lbrack {\sin^{- 1}( \frac{V}{a} )} \rbrack}},} & {V \leq a}\end{matrix}.} } & (5)\end{matrix}$

Similar to 3-level case, the AM-AM function of 5-level fixed thresholdPWM can be developed as

$\begin{matrix}{{x(a)} = \{ \begin{matrix}{0,} & {0 \leq a < V_{1}} \\{{\frac{2}{\pi}{\cos\lbrack {\sin^{- 1}( \frac{V_{1}}{a} )} \rbrack}},} & {V_{1} \leq a < V_{2}} \\{{\frac{2}{\pi}\{ {{\cos\lbrack {\sin^{- 1}( \frac{V_{1}}{a} )} \rbrack} + {\cos\lbrack {\sin^{- 1}( \frac{V_{2}}{a} )} \rbrack}} \}},} & {V_{2} \leq a}\end{matrix} } & (6)\end{matrix}$

This can be accordingly changed when non-uniform current distributionsare used for switching devices, to linearize by pre-distortion.

In order to meet the stringent linearity requirement of modern wirelesscommunications, the pre-distortion can be used to linearize thenonlinearity of PWM conversion. For 3-level PWM signal, thepre-distorted signal a can be

$\begin{matrix}{{a = {\frac{V}{\sin\lbrack {\cos^{- 1}( \frac{x}{4/\pi} )} \rbrack} = \frac{V}{\sqrt{1 - ( \frac{x}{4/\pi} )^{2}}}}},} & (7)\end{matrix}$

For 5-level PWM signal, the pre-distorted signal a could be

$\begin{matrix}{a = \{ \begin{matrix}{{{V_{1}{g_{1}(x)}} = {V_{1}\frac{1}{\sqrt{1 - ( {\frac{\pi}{2}x} )^{2}}}}},} & {0 \leq x \leq x_{0}} \\{{{V_{1}{g_{2}( {x,\alpha} )}} = {V_{1}\frac{\sqrt{1 + \alpha^{2} + {\frac{4}{\pi\; x}\sqrt{( {1 - \alpha^{2}} )^{2} + ( {\frac{\pi}{2}x\;\alpha} )^{2}}}}}{\alpha\sqrt{2^{2} - ( {\frac{\pi}{2}x} )^{2}}}}},} & {{x_{0} < x \leq \frac{4}{\pi}},}\end{matrix} } & (8) \\{\mspace{79mu}{where}} & \; \\{\mspace{79mu}{{\alpha = \frac{V_{1}}{V_{2}}},\mspace{14mu}{{{and}\mspace{14mu} x_{0}} = {{\frac{2}{\pi}{\cos( {\sin^{- 1}(\alpha)} )}} = {\frac{2}{\pi}{\sqrt{1 - \alpha^{2}}.}}}}}} & \;\end{matrix}$

Since both the in-phase (I) and quadrature (Q) components of the inputsignal, x_(I) and x_(Q), are normally distributed, the transmittedsignal is a complex Gaussian variable. The envelope x=√{square root over(x_(I) ²+x_(Q) ²)}, is Rayleigh distributed. The probability densityfunction of the Rayleigh fitted input envelope signal is PDF

${{f_{x}(x)} = {\frac{x}{\sigma^{2}}{\mathbb{e}}^{- \frac{x^{2}}{2\sigma^{2}}}}},{{{CDF}\mspace{11mu}{F_{x}(x)}} = {1 - {{\mathbb{e}}^{- \frac{x^{2}}{2\sigma^{2}}}.}}}$The scale parameter σ is calculated from

$\sqrt{\frac{2}{\pi}}E{\{ x \}.}$

For future computation convenience, define the partial moment as

$\begin{matrix}{{{M_{m}(x)} = {{\int_{0}^{x}{t^{m}{f_{x}(t)}\ {\mathbb{d}t}}} = {( {2\sigma^{2}} )^{m/2}( {{\Gamma( {{1 + \frac{m}{2}},0} )} - {\Gamma( {{1 + \frac{m}{2}},\frac{x^{2}}{2\sigma^{2}}} )}} )}}},} & (9)\end{matrix}$where Γ(z,a)=∫_(a) ^(∞)t^(z-1)e^(−t)dt is the incomplete gamma function.From (9), determine

$\begin{matrix}{{{M_{1}(x)} = {{\sqrt{\frac{{\pi\sigma}^{2}}{2}}{{erf}( \frac{x}{\sqrt{2\sigma^{2}}} )}} - {x\;{\mathbb{e}}^{- \frac{x^{2}}{2\sigma^{2}}}}}},{{M_{2}(x)} = {{2\sigma^{2}} - {( {{2\sigma^{2}} + x^{2}} ){\mathbb{e}}^{- \frac{x^{2}}{2\sigma^{2}}}}}},{{M_{3}(x)} = {{3\sqrt{\frac{{\pi\sigma}^{6}}{2}}{{erf}( \frac{x}{\sqrt{2\sigma^{2}}} )}} - {{x( {{3\sigma^{2}} + x^{2}} )}{\mathbb{e}}^{- \frac{x^{2}}{2\sigma^{2}}}}}},} & (10)\end{matrix}$where the error function erf(•) is defined as

${{erf}(x)} = {\frac{2}{\sqrt{\pi}}{\int_{0}^{x}{{\mathbb{e}}^{- t^{2}}{{\mathbb{d}t}.}}}}$

The power coding efficiency function is the power ratio of the desiredin-band over the whole band in frequency spectrum domain. For amodulated signal, the average power of the in-band signal x_(PS)(t)=xcos(2λf_(c)t) is

$\begin{matrix}{{P_{S}(x)} = {\frac{1}{2}E{\{ x^{2} \}.}}} & (11)\end{matrix}$

The total signal power equals to the waveform mean square power in thetime domain. For 3-level and 5-level,

$\begin{matrix}\begin{matrix}{{P_{{tot}\;\_\; 3}(x)} = {E\{ {2f_{I\; F}{W(t)}} \}}} \\{= {E{\{ {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{th}}{a} )}}} \} \cdot {Prob}}\{ {a \geq V_{th}} \}}} \\{= {E{\{ {1 - {\frac{2}{\pi}\cos^{- 1}( \frac{x}{4/\pi} )}} \}.}}}\end{matrix} & (12) \\\begin{matrix}{{P_{{tot}\;\_ 5}(x)} = {E\{ {\frac{1}{T}{\int_{0}^{T}{{f(t)}^{2}{\mathbb{d}t}}}} \}}} \\{= {{E\{ {2\;{f_{I\; F}\lbrack {{{W_{2}(t)} \cdot 1^{2}} + {( {{W_{1}(t)} - {W_{2}(t)}} ) \cdot 0.5^{2}}} \rbrack}} \}} +}} \\{= {{\frac{1}{4}E\{ {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{1}}{a} )}}} \}} + {\frac{3}{4}E{\{ {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{2}}{a} )}}} \} \cdot}}}} \\{{Prob}{\{ {a > V_{2}} \}.}}\end{matrix} & (13)\end{matrix}$

The general form of the average coding efficiency is

$\begin{matrix}{\eta_{C\; O\; D\; E} = {\frac{P_{s}(x)}{P_{{tot}\;\_ 3}(x)} = {\frac{\frac{1}{2}{\int_{0}^{1}{x^{2}{f_{x}(x)}{\mathbb{d}x}}}}{\int_{0}^{1}{\lbrack {1 - {\frac{2}{n}{\cos^{- 1}( \frac{x}{4/\pi} )}}} \rbrack{f_{x}(x)}{\mathbb{d}x}}}.}}} & (14) \\{{\eta_{C\; O\; D\; E} = {\frac{P_{s}(x)}{P_{{tot}\;\_ 5}(x)} = \frac{\frac{1}{2}{\int_{0}^{1}{x^{2}{f_{x}(x)}{\mathbb{d}x}}}}{\begin{matrix}{{\frac{1}{4}E\{ {1 - {\frac{2}{n}{\sin^{- 1}( \frac{V_{1}}{a} )}}} \}} + {\frac{3}{4}E}} \\{{\{ {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{2}}{a} )}}} \} \cdot {Prob}}\{ {a > V_{2}} \}}\end{matrix}}}},} & (15)\end{matrix}$where a is expressed in (8),

The P_(tot) _(—) ₅(x) can be written as

$\begin{matrix}{{{\frac{1}{4}{E\lbrack {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{1}}{a} )}}} \rbrack}} + {\frac{3}{4}{\underset{a > V_{2}}{E}\lbrack {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{V_{2}}{a} )}}} \rbrack}}} = {{\frac{1}{4}{\int_{0}^{x_{0}}{( {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{1}{g_{1}(x)} )}}} ){f_{x}(x)}{\mathbb{d}x}}}} + {\frac{1}{4}{\int_{x_{0}}^{\frac{4}{\pi}}{( {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{1}{g_{2}( {x,\alpha} )} )}}} ){f_{x}(x)}{\mathbb{d}x}}}} + {\frac{3}{4}{\int_{x_{0}}^{\frac{4}{\pi}}{( {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{1}{\alpha\;{g_{2}( {x,\alpha} )}} )}}} ){f_{x}(x)}{{\mathbb{d}x}.}}}}}} & (16)\end{matrix}$

Based on Equation (14), the power coding efficiency of 3-level PWMsignal depends only on the signal statistical property (i.e. f_(x)(x)).For 5-level PWM signal, in Equations (15) and (16), besides the signalstatistical property f_(x)(x), the power coding efficiency is alsoassociated with another parameter, a ratio α of values of voltagethresholds. Usually f_(x)(x) is given from the specific input signal.The ratio α is a design parameter that can be optimized to minimize theP_(tot) _(—) ₅(x), which lead to the maximum power coding efficiencyaccording to Equation (15).

Some embodiments perform several approximations of determination of thecoding efficiency as follows:

Consider

${1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{1}{g_{1}(x)} )}}} = {1 - {\frac{2}{\pi}{\sin^{- 1}( \sqrt{1 - ( {\frac{\pi}{2}x} )^{2}} )}}}$in the first term of metric (16), the 3^(rd) order Taylor seriesexpansion (at x=0) is given as:

${taylor} = {x + {\frac{1}{6}{( {\frac{\pi}{2}x} )^{3}.}}}$Therefore, the first term of metric (16) can be approximated as

$\begin{matrix}{{\frac{1}{4}{\int_{0}^{x_{0}}{( {x + {\frac{1}{6}( {\frac{\pi}{2}x} )^{3}}} ){f_{x}(x)}{\mathbb{d}x}}}} = {{\frac{1}{4}{M_{1}( x_{0} )}} + {\frac{1}{3}( \frac{\pi}{4} )^{3}{{M_{3}( x_{0} )}.}}}} & (17)\end{matrix}$Consider

$1 - {\frac{2}{\pi}\sin^{- 1}\frac{1}{g_{2}( {x,\alpha} )}}$in the second term of metric (16), the 3^(rd) order Taylor seriesexpansion (at x=0) is given as:

${taylor} = {1 - {\frac{2}{\pi}{\sin^{- 1}(\alpha)}} + {\frac{\alpha}{2x_{0}}( {x - x_{0}} )^{2}} - {\frac{\alpha^{3}}{2\; x_{0}^{2}}{( {x - x_{0}} )^{3}.}}}$

Therefore, the second term of metric (16) can be approximated as

$\begin{matrix}{{\frac{1}{4}{\int_{x_{0}}^{\frac{4}{\pi}}{( {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{1}{g_{2}( {x,\alpha} )} )}}} ){f_{x}(x)}{\mathbb{d}x}}}} = {{\frac{1}{4}( {1 - {\frac{2}{\pi}{\sin^{- 1}(\alpha)}} + \frac{\alpha\; x_{0}}{2}} )( {1 - {F_{x}( x_{0} )}} )} - {\frac{\alpha}{4}( {{M_{1}( {4/\pi} )} - {M_{1}( x_{0} )}} )} + {\frac{\alpha}{8\; x_{0}}{( {{M_{2}( {4/\pi} )} - {M_{2}( x_{0} )}} ).}}}} & (18)\end{matrix}$Consider

$1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{1}{\alpha\;{g_{2}( {x,\alpha} )}} )}}$in the last term of metric (16), the 3^(rd) order Taylor seriesexpansion (at x=0) is given as:

${taylor} = {( {x - x_{0}} ) - {\frac{\alpha^{2}}{2\; x_{0}}( {x - x_{0}} )^{2}} + {\frac{( {1 - \alpha^{2} + {3\;\alpha^{4}}} )}{6\; x_{0}^{2}}{( {x - x_{0}} )^{3}.}}}$

Therefore, the last term of metric (16) can be approximated as

$\begin{matrix}{ {{\frac{3}{4}{\int_{x_{0}}^{\frac{4}{\pi}}{( {1 - {\frac{2}{\pi}{\sin^{- 1}( \frac{1}{\alpha\;{g_{2}( {x,\alpha} )}} )}}} ){f_{x}(x)}{\mathbb{d}x}}}} = {{{- x_{0}}\frac{9}{8}( {1 + \alpha^{4}} )( {1 - {F_{x}( x_{0} )}} )} + {\frac{3}{8}( {3 + \alpha^{2} + {3\alpha^{4}}} )( {{M_{1}( {4/\pi} )} - {M_{1}( x_{0} )}} )}}} ) - {\frac{1 + {2\alpha^{2}} + {3\alpha^{4}}}{8\; x_{0}}( {{M_{2}( {4/\pi} )} - {M_{2}( x_{0} )}} )} + {\frac{1 - \alpha^{2} + {3\alpha^{4}}}{8\; x_{0}^{2}}{( {{M_{3}( {4/\pi} )} - {M_{3}( x_{0} )}} ).}}} & (19)\end{matrix}$

The approximated metric can also be formed by plugging (17), (18), and(19) into (16), to receive

$\begin{matrix}{{{\min\limits_{\alpha}{\frac{1}{4}{M_{1}( x_{0} )}}} + {\frac{1}{3}( \frac{\pi}{4} )^{3}{M_{3}( x_{0} )}} + {\frac{1}{4}( {1 - {\frac{2}{\pi}{\sin^{- 1}(\alpha)}} + \frac{\alpha\; x_{0}}{2}} )( {1 - {F_{x}( x_{0} )}} )} - {\frac{\alpha}{4}( {{M_{1}( {4/\pi} )} - {M_{1}( x_{0} )}} )} + {\frac{\alpha}{8\; x_{0}}( {{M_{2}( {4/\pi} )} - {M_{2}( x_{0} )}} )} - {\frac{3\; x_{0}}{4}\frac{2 + \alpha^{2}}{2}( {1 - {F_{x}( x_{0} )}} )} + {\frac{3( {1 + \alpha^{2}} )}{4}( {{M_{1}( {4/\pi} )} - {M_{1}( x_{0} )}} )} - {\frac{3\alpha^{2}}{8x_{0}}( {{M_{2}( {4/\pi} )} - {M_{2}( x_{0} )}} )}},} & (20)\end{matrix}$where M₁(•), M₂(•), and M₃(•) are expressed in (10).

Computation shows that with ratio α=0.3˜0.4 there is a minimum solutionof (20). Moreover, further computation demonstrates that, this optimumspot exists for all σ=0.1, 0.2, . . . , 0.9. Therefore, the ratio α=0.35can be used for various scenarios for 5-level fixed threshold PWM. Oncethe optimized thresholds ratio is determined, some embodiments selectset of voltage threshold values for implementing the optimum LUTpre-distortion unit and multi-level power encoder.

FIG. 10 shows a flow chart of a method for dynamically selecting the setof voltage thresholds according to some embodiments of the invention.The input signal data 1001 is fitted 1002 by Rayleigh distribution todetermine the scale parameter σ. The probability density function (PDF)and the cumulative distribution function (CDF) are determined 1003 usingthe scale parameter σ. Next, the partial moment functions are calculated1004 using the PDF.

The fixed threshold PWM power encoder is modeled 1005 by the AM-AMfunction. For example, pre-distortion block is modeled 1006 by theinverse function of the AM-AM function. The theoretical power codingefficiency target function is determined 1007.

In some embodiments, the method splits 1008 based on quantization levelsof the PWM signal. For 3-level case, the power coding efficiency 1011can be directly calculated. For 5-level case, the target function 1007is optimized by minimizing the total signal power 1009. The optimumthresholds ratio 1010 is determined to produce the 5 or more-level powercoding efficiency 1011. In one embodiment, the processor determines, foreach frame of the distorted input signal, the set of fixed threshold,the transformation function, and the LUT.

Although the invention has been described by way of examples ofpreferred embodiments, it is to be understood that various otheradaptations and modifications can be made within the spirit and scope ofthe invention. Therefore, it is the object of the appended claims tocover all such variations and modifications as come within the truespirit and scope of the invention.

We claim:
 1. A power encoder, comprising: a pulse width modulator formodulating a signal according to a set of thresholds including at leastfive voltage thresholds to produce a pulse width modulated (PWM) signalhaving at least five levels; and a switch mode power amplifier foramplifying the PWM signal by switching states of switching devicesaccording to amplitudes of the PWM signal, wherein at least one orcombination of a distribution of values of the voltage thresholds in theset and a distribution of values of a current generated by differentswitching devices are non-uniform, wherein in the non-uniformdistribution of values of the voltage thresholds a distance betweenvalues of a first pair of neighboring voltage thresholds does not equala distance between values of a second pair of neighboring voltagethresholds; wherein the set of threshold includes a first voltagethresholds V1 for a first level of the PWM signal and a second voltagethreshold V2 for a second level of the PWM signal, wherein a ratioav=V1/V2 is between 0.3 and 0.4 inclusively; and wherein the poweramplifier includes a first switching device for generating a currentwith a first value I1, such that the power amplifier produces I1 currentfor the first level of the PWM signal, wherein the power amplifierincludes a second switching device for generating a current with asecond value I2, such that the power amplifier produces I1+I2 currentfor the second level of the PWM signal, wherein a ratio ai=I1/(I1+I2) isbetween 0.2 and 0.4 inclusively.
 2. The power encoder of claim 1,wherein the set of thresholds includes a first voltage threshold and asecond voltage threshold, wherein a ratio of the first voltage thresholdand the second voltage threshold is between 0.3 and 0.4.
 3. The powerencoder of claim 2, wherein the ratio is 0.35.
 4. The power encoder ofclaim 1, wherein the switching devices of the power amplifier includetransistors having different dimensions to produce different currents.5. The power encoder of claim 1, wherein the PWM signal has (2n+1)levels, n is a positive natural number, wherein the set of thresholdsincludes n non-zero values of voltage thresholds, and wherein the poweramplifier includes 2n switching devices with non-uniform total currentcapability for the n non-zero levels of the PWM signal.
 6. The powerencoder of claim 1, wherein the PWM signal has (2n+1) levels, n is apositive natural number, wherein the set of thresholds includes nnon-zero values V_(n) of the voltage thresholds, and wherein the poweramplifier includes 2n switching devices for the n non-zero levels of thePWM signal to produce I_(n) current for each level, wherein a ratioa_(v)=V_(n-1)/V_(n) and a ratio a_(i)=I_(n-1)/(I_(n-1)+I_(n)) is between0.2 and 0.4 inclusively.
 7. The power encoder of claim 1, furthercomprising: an amplitude-phase splitter for splitting an input signalinto an envelope signal and a phase modulated signal; a pre-distortionunit for distorting the envelope signal using a look-up table (LUT) toproduce a distorted envelope signal, wherein the look-up table stores anon-linear mapping of a transformation function; a digital converter forcombining the distorted envelope signal with the phase modulated signalto produce a distorted input signal, wherein the signal is the distortedinput signal, such that the modulator modulates the distorted inputsignal according to a transformation function with the set of thresholdsto produce the PWM signal, wherein a relationship between the distortedinput signal and the PWM signal is non-linear.
 8. The power encoder ofclaim 7, wherein the modulator is a radio frequency (RF) modulator, andthe digital converter up-converts the distorted envelope signal and thephase modulated signal with an RF carrier signal, such that the PWMsignal is an RF pulse train.
 9. The power encoder of claim 7, whereinthe modulator is an intermediate frequency (IF) modulator, and thedigital converter up-converts the distorted envelope signal and thephase modulated signal with an IF carrier signal, such that the PWMsignal is an IF pulse train.
 10. The power encoder of claim 9, furthercomprising: a second digital up-converter for converting the IF pulsetrain to a radio frequency (RF) pulse train and for submitting the RFpulse train to the switch mode power amplifier.
 11. The power encoder ofclaim 7, wherein a value of each threshold is based on a probabilitydensity function (PDF) of a portion of the input signal.
 12. The powerencoder of claim 11, further comprising a memory for storing a frame ofthe distorted input signal; a processor for determining the PDF fromdata in the frame, for integrating the PDF to generate a curve of acumulative distribution function (CDF), and for selecting values of eachfixed threshold based on the curve.
 13. The power encoder of claim 12,wherein the processor determines, for each frame of the distorted inputsignal, the set of fixed thresholds, the transformation function, andthe LUT.
 14. A method for power encoding, comprising: modulating asignal according to a set of thresholds including at least two positivevoltage thresholds to produce a pulse width modulated (PWM) signalhaving at least five levels; and amplifying the PWM signal by switchingstates of switching devices according to amplitudes of the PWM signal,wherein at least one or combination of a distribution of values of thevoltage thresholds in the set and a distribution of values of a currentgenerated by different switching devices are non-uniform, wherein in thenon-uniform distribution of values of the voltage thresholds a distancebetween values of a first pair of neighboring voltage thresholds doesnot equal a distance between values of a second pair of neighboringvoltage thresholds; wherein the set of threshold includes a firstvoltage thresholds V1 for a first level of the PWM signal and a secondvoltage threshold V2 for a second level of the PWM signal, wherein aratio av=V1/V2 is between 0.3 and 0.4 inclusively; and wherein theamplifying is performed with a power amplifier including a firstswitching device for generating a current with a first value I1, suchthat the power amplifier produces I1 current for the first level of thePWM signal, and second switching device for generating a current with asecond value I2, such that the power amplifier produces I1+I2 currentfor the second level of the PWM signal, wherein a ratio ai=I1/(I1+I2) isbetween 0.2 and 0.4 inclusively.
 15. The method of claim 14, wherein theset of thresholds includes a first voltage threshold and a secondvoltage threshold, wherein a ratio of the first voltage threshold andthe second voltage threshold is between 0.3 and 0.4.
 16. The method ofclaim 15, wherein the ratio is 0.35.
 17. The method of claim 15, whereinthe amplifying is performed with transistors having different dimensionsto produce different currents.
 18. The method of claim 14, wherein thePWM signal is an intermediate frequency (IF) pulse train, furthercomprising: converting the IF pulse train to a radio frequency (RF)pulse train for the amplifying.